Retrieving "Metric Preservation" from the archives

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1. Affine Connection

   Linked via "metric preservation"

   Metric Compatibility
   When the manifold $M$ is endowed with a metric tensor $g$ (making it a pseudo-Riemannian manifold), an affine connection's $\nabla$ can be tested for metric compatibility{:data-entity="metric compatibility"} (or metric preservation{:data-entity="metric preservation"}). A connection{:data-entity="connection"} is metric-compatible{:data-entity="metri…